The determing factor for what type of weapon you can hunt with is determined by the class (A or B) and not the restrictions. Technically, your permit only allows you to go target shooting and you could potentially be in trouble (maybe not jail time), but you could loose your permit if caught hunting without the proper license. The determing factor for what type of weapon you can hunt with is determined by the class (A or B) and not the restrictions.
I'd call ASAP and tell the Chief that you intend on hunting and you had requested an ALP license. Politely request an ALP (because it covers hunting and target shooting) and if he pushes back, get hunting and target shooting statement. You paid a lot for your license and it needs to be valid.
If you do not do this immediately, your Chief may require that you reapply. This all assumes you are a resident of MA. If you aren't a non-resident, you typically get an ALP class A.
Good luck.